Elasticity-based-exfoliability measure for high-throughput computational exfoliation of two-dimensional materials

Two-dimensional (2D) materials are promising candidates for uses in next-generation electronic and optoelectronic devices. However, only a few high-quality 2D materials have been mechanically exfoliated to date. One of the critical issues is that the exfoliability of 2D materials from their bulk precursors is unknown. To assess the exfoliability of potential 2D materials from their bulk counterparts, we derived an elasticity-based-exfoliability measure based on an exfoliation mechanics model. The proposed measure has a clear physical meaning and is universally applicable to all material systems. We used this measure to calculate the exfoliability of 10,812 crystals having a first-principles calculated elastic tensor. By setting the threshold values for easy and potential exfoliation based on already-exfoliated materials, we predicted 58 easily exfoliable bulk crystals and 90 potentially exfoliable bulk crystals for 2D materials. As evidence, a topology-based algorithm indicates that there is no interlayer bonding topology for 93% predicted exfoliable bulk crystals, and the analysis on packing ratios shows that 99% predicted exfoliable bulk crystals exhibit a relatively low packing ratio value. Moreover, literature survey shows that 34 predicted exfoliable bulk crystals have been experimentally exfoliated into 2D materials. In addition, the characteristics of these predicted 2D materials were discussed for practical use of such materials.

Integrating Elastic Tensor and PC-SAFT Modeling with Systems-Based Pharma 4.0 Simulation, to Predict Process Operations and Product Specifications of Ternary Nanocrystalline Suspensions

Comminution of BCS II APIs below the 1 μm threshold followed by solidification of the obtained nanosuspensions improves their dissolution properties. The breakage process reveals new crystal faces, thus creating altered crystal habits of improved wettability, facilitated by the adsorption of stabilizing polymers. However, process-induced transformations remain unpredictable, mirroring the current limitations of our atomistic level of understanding. Moreover, conventional equations of estimating dissolution, such as Noyes–Whitney and Nernst–Brunner, are not suitable to quantify the solubility enhancement due to the nanoparticle formation; hence, neither the complex stabilizer contribution nor the adsorption influence on the interfacial tension occurring between the water and APIs is accounted for. For such ternary mixtures, no numeric method exists to correlate the mechanical properties with the interfacial energy, capable of informing the key process parameters and the thermodynamic stability assessment of nanosuspensions. In this work, an elastic tensor analysis was performed to quantify the API stability during process implementation. Moreover, a novel thermodynamic model, described by the stabilizer-coated nanoparticle Gibbs energy anisotropic minimization, was structured to predict the material’s system solubility quantified by the application of PC-SAFT modeling. Comprehensively merging elastic tensor and PC-SAFT analysis into the systems-based Pharma 4.0 algorithm provided a validated, multi-level, built-in method capable of predicting the critical material quality attributes and corresponding key process parameters.

Identification of the Orthotropic Elastic Tensor of Composites Using Full Field Lamb Wave Energy Velocities and Dispersion Curves

A multi-objective inversion procedure is proposed based on 3D Lamb wave dispersion curves and energy velocity matching to identify the elastic stiffness tensor of orthotropic composite plates. To validate the procedure, finite element model simulations and experimental measurements have been conducted on an aluminum and a composite plate by using piezoelectric actuator broadband signals. Experimentally, the in-plane and out-of-plane velocity components on the surface of these plates were measured using a 3D Infrared Scanning Laser Doppler Vibrometer. By exploiting Fourier Transform, the measured space-time domain data is converted into the frequency-wavenumber domain, from which dispersion curves are extracted. To identify the energy velocity, Short Time Fourier Transform and linear Radon transformation have been applied. Then, image processing is used both for dispersion and energy velocity curves to match the amplitude of the in-plane and out-of-plane velocities on the surface of the plate. The Semi Analytical Finite Element method (SAFE) was selected as the forward model to be embedded in an inversion algorithm due to its accuracy and robustness. Using a multi-objective genetic algorithm, the elastic tensor is calculated by simultaneously minimizing the error between (i) the measured and calculated dispersion curves on one hand, and (ii) the measured and calculated energy velocity slowness curves on the other hand for every in and out of plane velocity measurement. The mean values of the pareto front are selected as optimum parameters. The reconstructed elastic stiffness properties show good agreement with less than 6% average deviation.

Phenomenological models for estimating and constraining c13 for transversely isotropic hydrocarbon source rocks

Hydrocarbon source rocks can be adequately approximated as transversely isotropic (TI) media. The elastic properties of a TI medium are defined by five stiffness parameters: c11, c33, c44, c66, and c13. The laboratory estimation of c11, c33, c44, and c66 is straightforward, with each of the stiffness parameters determined by a single velocity measurement in an orthogonal direction. For c13, we need the information of c11, c33, c44, and at least one oblique velocity. Consequently, it is usually more difficult to estimate c13 than the other stiffness parameters in the laboratory, and it is even more challenging to acquire it from the field. Therefore, it is important to find the relations between c13 and the other stiffness parameters so that c13 can be estimated from the orthogonal elastic tensor elements c11, c33, c44, and c66 that can be much more economically and reliably acquired. There are phenomenological models for estimating c13 from the other stiffness parameters, but their accuracy is not always satisfactory. We found that c13 has strong correlations with c33 − 2 c44 and c11 − 2 c66, and that c33 − 2 c44 generally underestimates c13 and c11 − 2 c66 generally overestimates c13. The average of c33 − 2 c44 and c11 − 2 c66 can be a much more precise phenomenological model to approximate c13. We also found that c11 − 2 c66 is generally greater than c33 − 2 c44 for hydrocarbon source rocks. Therefore, we evaluated that c13 should lie between c33 − 2 c44 and c11 − 2 c66 for hydrocarbon source rocks.

Geodynamic Tomography: Constraining Upper-Mantle Deformation Patterns from Bayesian Inversion of Surface Waves

<p>In the Earth’s upper mantle, seismic anisotropy mainly originates from the crystallographic preferred orientation (CPO) of olivine due to mantle deformation. Large-scale observation of anisotropy in surface wave tomography models provides unique constraints on present-day mantle flow. However, surface waves are not sensitive to the 21 coefficients of the elastic tensor, and therefore the complete anisotropic tensor cannot be resolved independently at every location. This large number of parameters may be reduced by imposing spatial smoothness and symmetry constraints to the elastic tensor. In this work, we propose to regularize the tomographic problem by using constraints from geodynamic modeling to reduce the number of model parameters. Instead of inverting for seismic velocities, we parametrize our inverse problem directly in terms of physical quantities governing mantle flow: a temperature field, and a temperature-dependent viscosity. The forward problem consists of three steps: (1) calculation of mantle flow induced by thermal anomalies, (2) calculation of the induced CPO and elastic properties using a micromechanical model, and (3) computation of azimuthally varying surface wave dispersion curves. We demonstrate how a fully nonlinear Bayesian inversion of surface wave dispersion curves can retrieve the temperature and viscosity fields, without having to explicitly parametrize the elastic tensor. Here, we consider simple flow models generated by spherical temperature anomalies. The results show that incorporating geodynamic constraints in surface wave inversion help to retrieve patterns of mantle deformation. The solution to our inversion problem is an ensemble of models (i.e. thermal structures) representing a posterior probability, therefore providing uncertainties for each model parameter.</p>

Micromechanics Approach for the Overall Elastic Properties of Ceramic Matrix Composites Incorporating Defect Structures

Initial mechanical behavior of Ceramic Matrix Composites (CMCs) is linear until the proportional limit. This initial behavior is characterized by linear elastic properties, which are anisotropic due to the orientation and arrangement of fibers in the matrix. The linear elastic properties are needed during analysis and design of CMC components. CMCs are made with ceramic unidirectional or woven fiber preforms embedded in a ceramic matrix formed via various processing routes. The matrix processing of interest in this work is the Polymer Impregnation and Pyrolysis (PIP) process. As this process involves pyrolysis to convert a pre-ceramic polymer into ceramic, considerable volume shrinkage occurs in the material. This leads to significant defects in the form of porosity of various size, shape, and volume fraction. These defect structures can have a significant impact on the elastic and damage response of the material. In this paper, we develop a new micromechanics modeling framework to study the effects of processing-induced defects on linear elastic response of a PIP-derived CMC. A combination of analytical and computational micromechanics approaches is used to derive the overall elastic tensor of the CMC as a function of the underlying constituents and/or defect structures. It is shown that the volume fraction and aspect ratio of porosity at various length-scales plays an important role in accurate prediction of the elastic tensor. Specifically, it is shown that the through-thickness elastic tensor components cannot be predicted accurately using the micromechanics models unless the effects of defects are considered.

On the stress dependence of the elastic tensor

Summary The dependence of the elastic tensor on the equilibrium stress is investigated theoretically. Using ideas from finite elasticity, it is first shown that both the equilibrium stress and elastic tensor are given uniquely in terms of the equilibrium deformation gradient relative to a fixed choice of reference body. Inversion of the relation between the deformation gradient and stress might, therefore, be expected to lead neatly to the desired expression for the elastic tensor. Unfortunately, the deformation gradient can only be recovered from the stress up to a choice of rotation matrix. Hence it is not possible in general to express the elastic tensor as a unique function of the equilibrium stress. By considering material symmetries, though, it is shown that the degree of non-uniqueness can sometimes be reduced, and in some cases even removed entirely. These results are illustrated through a range numerical calculations, and we also obtain linearised relations applicable to small perturbations in equilibrium stress. Finally, we make a comparison with previous studies before considering implications for geophysical forward- and inverse-modelling.

Geodynamic tomography: constraining upper-mantle deformation patterns from Bayesian inversion of surface waves

SUMMARY In the Earth’s upper mantle, seismic anisotropy mainly originates from the crystallographic preferred orientation (CPO) of olivine due to mantle deformation. Large-scale observation of anisotropy in surface wave tomography models provides unique constraints on present-day mantle flow. However, surface waves are not sensitive to the 21 coefficients of the elastic tensor, and therefore the complete anisotropic tensor cannot be resolved independently at every location. This large number of parameters may be reduced by imposing spatial smoothness and symmetry constraints to the elastic tensor. In this work, we propose to regularize the tomographic problem by using constraints from geodynamic modelling to reduce the number of model parameters. Instead of inverting for seismic velocities, we parametrize our inverse problem directly in terms of physical quantities governing mantle flow: a temperature field, and a temperature-dependent viscosity. The forward problem consists of three steps: (1) calculation of mantle flow induced by thermal anomalies, (2) calculation of the induced CPO and elastic properties using a micromechanical model, and (3) computation of azimuthally varying surface wave dispersion curves. We demonstrate how a fully nonlinear Bayesian inversion of surface wave dispersion curves can retrieve the temperature and viscosity fields, without having to explicitly parametrize the elastic tensor. Here, we consider simple flow models generated by spherical temperature anomalies. The results show that incorporating geodynamic constraints in surface wave inversion help to retrieve patterns of mantle deformation. The solution to our inversion problem is an ensemble of models (i.e. thermal structures) representing a posterior probability, therefore providing uncertainties for each model parameter.